Size of targets and use of header hierarchy in pop-up windows

Hi all,

as the e-mail subject suggests, I have trouble with two of the SC's from the WCAG. SC 2.4.10 Section Headings and SC 2.5.5 Target Size.
I'm working on a webpage where, after clicking on a link, a pop-up window appears with further information.
Regarding the SC 2.4.10, the header hierarchy to this point looks as follows:

<h1>Websites Header</h1>
<h2>Section 1</h2>
<h3>Link with further information.</h3>
....
<h2>Section 2</h2>
....

So my question is, do I have to continue with an h4-tag in the pop-up window which is following the click on the link or does the hierarchy starts with h1 again?

Regarding the SC 2.5.5, I'm interested if the usage of an invisible plane that's 44x44px and lies beneath the target conforms to the SC. I'm not sure whether the clickable area must be visible or not, so do I need any kind of Frame around it?

Thanks for the help and best regards
Tim